Problem: A circle has a radius of $7$. An arc in this circle has a central angle of $180^\circ$. What is the length of the arc? ${14\pi}$ ${180^\circ}$ $\color{#DF0030}{7\pi}$ ${7}$
Solution: First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (7) = 14\pi$ The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{180^\circ}{360^\circ} = \dfrac{s}{14\pi}$ $\dfrac{1}{2} = \dfrac{s}{14\pi}$ $\dfrac{1}{2} \times 14\pi = s$ $7\pi = s$